This has been a point of some controversy within our local AL community, with different DMs giving different rulings. From what I could see, this site has only touched on the Maneuver/Smite issue, with, according to some of my DMs, an out of date answer.

This also leaves the problem of extra dice on magical weapons such as an Ild rune or Hazirawn, maneuver damage dice given by another player through Commander's Strike, damage dice given by a College of Valor bard, Sneak Attack dice, and likely others which currently escape my mind.

Which damage dice exactly does the Great Weapon Fighting fighting style allow you to reroll?

3 Answers
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If you use Great Weapon Fighting with a feature like Divine Smite or a spell like hex, do you get to reroll any 1 or 2 you roll for the extra damage?
The Great Weapon Fighting feature—which is shared by fighters and paladins—is meant to benefit only the damage roll of the weapon used with the feature. For example, if you use a greatsword with the feature, you can reroll any 1 or 2 you roll on the weapon’s 2d6. If you’re a paladin and use Divine Smite with the greatsword, Great Weapon Fighting doesn’t let you reroll a 1 or 2 that you roll for the damage of Divine Smite.

Also: As pointed out by Doval, Jeremy Crawford allows all weapon dices to be rerolled. This includes, for instance, a Frost Brand sword's additional cold damage, since that damage is part of the weapon's damage itself (not from an additional feature).

I called Wizards of the Coast for an official answer, which I'll summarize.

How Great Weapon Fighting works is that it lets the player who has the GWF fighting style and is using a melee weapon two-handed can reroll all of the damage associated with that weapon.

For example, some weapons that fall under this category are a greatsword or maul, flame tongue, frost brand, vorpal sword, and the sentient weapon Hazirawn from the Hoard of the Dragon Queen adventure. Even the extra damage coming from those weapons can be rerolled as per the Great Weapon Fighting fighting style.

The spells that also allow for this effect are elemental weapon and holy weapon. Specifically because they turn the weapon into a magical weapon that does additional weapon damage.

However, while all of these weapons and spells allow rerolls, what doesn't allow rerolls are literally whatever isn't coming from the weapon. Divine Smite, the half orc's Brutal Critical trait (boo, I know, but I don't think anyone really cares about that one), the rogue's Sneak Attack feature, the hex spell, and the hunter's mark spell are all features that have been under debate, and all of them don't allow rerolls by the rules.

However, having said all of that, I stress that while at a table, the DM has the ultimate authority to allow or not allow this or that rule into the game. Hope I helped clarify how the rules worked to a degree.

\$\begingroup\$"When you roll a 1 or 2 on a damage die for an attack you make with a melee weapon." I agree that the reroll only applies to the weapon damage dice but I don't agree with how you came to the conclusion. The quote you provide could easily be interpreted as "a 1 or 2 on any damage die for an attack you make, as long as the attack was made with a melee weapon." It is exactly this sentence that creates the confusion so I don't see how it can be used to answer the question.\$\endgroup\$
– LegendaryDudeJan 31 '17 at 14:04

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\$\begingroup\$@LegendaryDude And that interpretation you have at the end is how my table reads it. Rolling dice is fun and when you're Divine Smiting it makes you feel even better :)\$\endgroup\$
– NautArchJan 31 '17 at 18:42